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Singularités nilpotentes et intégrales premières.

Rafik MezianiPaulo Sad — 2007

Publicacions Matemàtiques

This paper presents a classification of plane dicritical nilpotent singularities, i.e. singularities which have nilpotent linear part and infinitely many separatrices. In particular the existence of meromorphic first integrals is discussed. The same ideas are applied to other kind of dicritical singularities.

On dicritical foliations and Halphen pencils

Luís Gustavo MendesPaulo Sad — 2002

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

The aim of this article is to provide information on the number and on the geometrical position of singularities of holomorphic foliations of the projective plane. As an application it is shown that certain foliations are in fact Halphen pencils of elliptic curves. The results follow from Miyaoka’s semipositivity theorem, combined with recent developments on the birational geometry of foliations.

Fonctions et feuilletages Levi-Flat. Étude locale

Dominique CerveauPaulo R. Sad — 2004

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We define the notion of CR equivalence for Levi-flat foliations and compare in a local setting these foliations to their linear parts. We study also the situation where the foliation has a first integral ; a condition is given so that this integral is the real part of a holomorphic function.

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